A curious instability phenomenon for a rounded corner in presence of a negative material

Lucas Chesnel (1) , Xavier Claeys (2, 3) , Sergueï A. Nazarov (4)

1 Department of Mathematics and Systems Analysis [Aalto]
2 LJLL - Laboratoire Jacques-Louis Lions
3 ALPINES - Algorithms and parallel tools for integrated numerical simulations
4 IPME - Institute of Mechanical Engineering Problems [St. Petersburg]

We study a 2D transmission problem between a positive material and a negative material. In electromagnetics, this negative material can be a metal at optical frequencies or a negative metamaterial. We highlight an unusual instability phenomenon in some configurations: when the interface between the two materials presents a rounded corner, it can happen that the solution depends critically on the value of the rounding parameter. To prove this result, we provide an asymptotic expansion of the solution, when it is well-defined, in the geometry with a rounded corner. Then, we demonstrate that the asymptotic expansion is not stable with respect to the rounding parameter. We end this paper with a numerical illustration of this instability phenomenon.

Mots clés: sign-changing coefficients.; plasmonic; metamaterial; sign-changing coefficients; Negative materials; corner

Domaines: Analyse numérique [math.NA]

Lucas Chesnel, Xavier Claeys, Sergueï A. Nazarov. A curious instability phenomenon for a rounded corner in presence of a negative material. Asymptotic Analysis, 2014, 88 (1-2), pp.43-74. ⟨hal-00909836⟩